Microfluidic devices with integrated resistive heater electrodes including systems and methods for controlling and measuring the temperatures of such heater electrodes

ABSTRACT

The invention relates to methods and devices for control of an integrated thin-film device with a plurality of microfluidic channels. In one embodiment, a microfluidic device is provided that includes a microfluidic chip having a plurality of microfluidic channels and a plurality of multiplexed heater electrodes, wherein the heater electrodes are part of a multiplex circuit including a common lead connecting the heater electrodes to a power supply, each of the heater electrodes being associated with one of the microfluidic channels. The microfluidic device also includes a control system configured to regulate power applied to each heater electrode by varying a duty cycle, the control system being further configured to determine the temperature of each heater electrode by determining the resistance of each heater electrode.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of and claims priority topending U.S. patent application Ser. No. 12/165,043 filed on Jun. 30,2008, which claims the benefit of Provisional Patent Application Ser.No. 60/968,760, filed Aug. 29, 2007, the entire contents of which areincorporated herein by reference.

BACKGROUND

1. Field of Invention

The present invention relates to microfluidic devices and temperaturecontrol of the microfluidic devices for performing biological reactions.More specifically, the present invention relates to systems and methodsfor determining and controlling the temperature of integrated thin filmresistive heater elements in the microfluidic device.

2. Discussion of the Background

The detection of nucleic acids is central to medicine, forensic science,industrial processing, crop and animal breeding, and many other fields.The ability to detect disease conditions (e.g., cancer), infectiousorganisms (e.g., HIV), genetic lineage, genetic markers, and the like,is ubiquitous technology for disease diagnosis and prognosis, markerassisted selection, identification of crime scene features, the abilityto propagate industrial organisms and many other techniques.Determination of the integrity of a nucleic acid of interest can berelevant to the pathology of an infection or cancer.

One of the most powerful and basic technologies to detect smallquantities of nucleic acids is to replicate some or all of a nucleicacid sequence many times, and then analyze the amplification products.Polymerase chain reaction (PCR) is a well-known technique for amplifyingDNA. With PCR, one can produce millions of copies of DNA starting from asingle template DNA molecule. PCR includes phases of “denaturation,”“annealing,” and “extension.” These phases are part of a cycle which isrepeated a number of times so that at the end of the process there areenough copies to be detected and analyzed. For general detailsconcerning PCR, see Sambrook and Russell, Molecular Cloning—A LaboratoryManual (3rd Ed.), Vols. 1-3, Cold Spring Harbor Laboratory, Cold SpringHarbor, N.Y. (2000); Current Protocols in Molecular Biology, F. M.Ausubel et al., eds., Current Protocols, a joint venture between GreenePublishing Associates, Inc. and John Wiley & Sons, Inc., (supplementedthrough 2005) and PCR Protocols A Guide to Methods and Applications, M.A. Innis et al., eds., Academic Press Inc. San Diego, Calif. (1990).

The PCR process phases of denaturing, annealing, and extension occur atdifferent temperatures and cause target DNA molecule samples toreplicate themselves. Temperature cycling (thermocyling) requirementsvary with particular nucleic acid samples and assays. In the denaturingphase, a double stranded DNA (dsDNA) is thermally separated into singlestranded DNA (ssDNA). During the annealing phase, primers are attachedto the single stranded DNA molecules. Single stranded DNA molecules growto double stranded DNA again in the extension phase through specificbindings between nucleotides in the PCR solution and the single strandedDNA. Typical temperatures are 95° C. for denaturing, 55° C. forannealing, and 72° C. for extension. The temperature is held at eachphase for a certain amount of time which may be a fraction of a secondup to a few tens of seconds. The DNA is doubled at each cycle; itgenerally takes 20 to 40 cycles to produce enough DNA for theapplications. To have good yield of target product, one has toaccurately control the sample temperatures at the different phases to aspecified degree.

More recently, a number of high throughput approaches to performing PCRand other amplification reactions have been developed, e.g., involvingamplification reactions in microfluidic devices, as well as methods fordetecting and analyzing amplified nucleic acids in or on the devices.Thermal cycling of the sample for amplification is usually accomplishedin one of two methods. In the first method, the sample solution isloaded into the device and the temperature is cycled in time, much likea conventional PCR instrument. In the second method, the sample solutionis pumped continuously through spatially varying temperature zones. See,for example, Lagally et al. (Analytical Chemistry 73:565-570 (2001)),Kopp et al. (Science 280:1046-1048 (1998)), Park et al. (AnalyticalChemistry 75:6029-6033 (2003)), Hahn et al. (WO 2005/075683),Enzelberger et al. (U.S. Pat. No. 6,960,437) and Knapp et al. (U.S.Patent Application Publication No. 2005/0042639).

Many detection methods require a determined large number of copies(millions, for example) of the original DNA molecule, in order for theDNA to be characterized. Because the total number of cycles is fixedwith respect to the number of desired copies, the only way to reduce theprocess time is to reduce the length of a cycle. Thus, the total processtime may be significantly reduced by rapidly heating and cooling samplesto process phase temperatures while accurately maintaining thosetemperatures for the process phase duration.

Accordingly, what is desired is a system and method for rapidly andaccurately changing process temperatures in PCR processes.

SUMMARY

The present invention relates to systems and methods for determining andcontrolling the temperature of integrated thin film resistive heaterelements in a microfluidic device for microfluidic thermal cycling.

In one aspect, the invention provides a method for determining theresistance of a sensor in a multiplexed sensor network including aplurality of sensors sharing a common lead for connecting each of theplurality of sensors to a power supply. In one embodiment, determiningthe resistance of the sensor includes: (a) sequentially measuring thecombined series resistances for N number of distinct sensor pairs, suchthat each of the plurality of sensors is included in at least one of themeasured sensor pairs, wherein N is the number of sensors in theplurality of sensors, and the measured sensor pairings are such that theindividual resistance of each of the plurality of sensors may bedetermined; and (b) determining for the individual resistance of atleast one of the plurality of sensors based upon the measured combinedseries resistances.

In some embodiments, determining for the resistance of at least one ofthe plurality of may include: (a) defining a first matrix correspondingto the measured combined series resistances; (b) defining a secondmatrix having rows and columns such that each column corresponds to asensor in the network and each row represents a measured sensor pairconfiguration; (c) generating an inverse matrix of the second matrix;and (d) multiplying the inverse of the second matrix by the firstmatrix. In some embodiments, the second matrix is defined by linearlyindependent equations such that the second matrix is of full rank.

In some embodiments, measuring a combined series resistance of a sensorpair may include: (a) electrically isolating the sensor pair from theother sensors in the plurality of sensors; (b) applying a source voltageor current to a first terminal electrically coupled to a first sensor ofthe sensor pair; and (c) measuring an output voltage at a secondterminal electrically coupled to a second sensor of the sensor pair.

In some embodiments, the measurements are performed in accordance withtiming instructions supplied by a control unit.

In some embodiments, the multiplexed sensor network is a component of amicrofluidic device and the sensors may be, for example, resistancetemperature detectors in thermal communication with a fluidic channel.

In some embodiments, the method may further include: (c) generating afeedback signal such as, for example, a signal that describes the statusof a biological process, based upon either the equivalent resistance ofa series combination of sensors or the resistance of an individualsensor; and (d) transmitting the feedback signal to a control unitconfigured to provide closed-loop thermal control.

In another aspect, the present invention provides a microfluidic devicefor performing biological reactions. In one embodiment, the microfluidicdevice includes: a microfluidic chip having a plurality of microfluidicchannels and a plurality of sensor elements, wherein the sensor elementsare connected in a multiplexed network that includes a shared commonlead; a control unit configured to sequentially measure the combinedseries resistances for N number of distinct sensor pairs; and aprocessor configured to determine the individual resistance of at leastone of the plurality of sensors based upon the measured combined seriesresistances. In some embodiments, each of the plurality of sensors isincluded in at least one of the measured sensor pairs, and wherein N isthe number of sensors in the plurality of sensors, and the measuredsensor pairings are such that the individual resistance of each of theplurality of sensors may be determined.

In some embodiments, the processor is further configured to define ameasurement matrix having rows and columns such that each columncorresponds to a single sensor in the network and each row describes ameasurement configuration applied by the control unit and, the processorbeing further adapted to determine the individual resistance of at leastone sensor in the network by multiplying the inverse of the measurementmatrix by a vector containing the measured combined series resistances.In some embodiments, the measurement matrix is of full rank.

In some embodiments, the microfluidic device also includes: a firstterminal electrically coupled to at least two sensors connected inseries; and a second terminal electrically coupled to the at least twosensors. In some embodiments, a voltage or current applied to the firstterminal generates a current or voltage at the second terminalrepresentative of the combined series resistance of the at least twosensors.

In some embodiments, the sensors are resistance temperature detectors.

In some embodiments, the control unit may be further adapted to heat theresistance temperature detectors by pulse width modulation.

The above and other embodiments of the present invention are describedbelow with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and form partof the specification, illustrate various embodiments of the presentinvention. In the drawings, like reference numbers indicate identical orfunctionally similar elements. Additionally, the left-most digit(s) ofthe reference number identifies the drawing in which the referencenumber first appears.

FIG. 1 depicts a graph illustrating a temperature versus time PCRprofile.

FIG. 2 depicts a perspective view of a microfluidic device embodyingaspects of the present invention.

FIG. 3 depicts an exploded perspective view of the microfluidic deviceof FIG. 2.

FIG. 4 depicts a partial perspective view of the microfluidic device ofFIG. 2 with a portion of the device shown enlarged.

FIG. 5 depicts a block diagram illustrating the various functional andcontrol regions of a microfluidic device.

FIG. 6 depicts representative pulse width modulation (PWM) controlprofiles for achieving various temperatures in the resistive heaterelectrodes of the microfluidic device.

FIG. 7 depicts PWM profiles for an eight-channel microfluidic device,wherein the eight resistive heater electrodes are electrically driven ina multiplexed sequence.

FIG. 8 depicts PWM profiles for a differential drive method forelectrically driving microfluidic thin film resistive heaters.

FIG. 9 depicts a representative thermal response to PWM drive signals oftwo microfluidic heater channels.

FIG. 10 depicts a flow chart showing a heater calibration method.

FIG. 11 depicts a flow chart showing a PWM control method wherebycalibration values are stored and utilized to compute optimum PWMconditions.

FIG. 12 depicts a circuit enabling temperature measurements in aresistive heater electrode during both the power-off and power-onportions of a PWM duty cycle.

FIG. 13 depicts three different duty cycle profiles, wherein each dutycycle ends at about the same time so there is a period during whichpower is off for all heaters of a multiplexed system.

FIG. 14 depicts a resistive network of a microfluidic device withmultiplexed resistive heaters, wherein the heater electrodes are usedfor both heating and temperature measurement.

FIG. 15 depicts a diagram of a circuit configured to selectivelydisconnect a common lead from a power supply, selectively connect any ofthe resistive heaters channels to the power supply, or selectivelyremove any of the heater channels from the multiplex circuit.

FIG. 16 depicts a flow chart showing a representative embodiment of amethod for determining the temperatures of a plurality of multiplexedheaters.

FIG. 17 depicts a flow chart showing a first alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 18 depicts a flow chart showing a second alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 19 depicts a flow chart showing a third alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 20 depicts a flow chart showing a fourth alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 21 depicts a flow chart showing a fifth alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 22 depicts a flow chart showing a method for PWM closed-loopcontrol of a resistive heater.

FIG. 23 depicts a flow chart showing a method for analog closed-loopcontrol of a resistive heater.

FIG. 24 depicts a flow chart showing a method for PWM closed-loopcontrol for heating different resistive heaters differently to accountfor manufacturing variations or temperature gradients.

FIG. 25 depicts a flow chart showing a method for open-loop control of aresistive heater electrode.

FIG. 26 depicts a plan view of a microfluidic device embodying aspectsof the present invention.

FIG. 27 depicts a flow chart showing an alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIG. 28 depicts a timing diagram for controlling switches to perform amethod for determining the temperatures of a plurality of multiplexedheaters.

FIG. 29 depicts a flow chart showing an alternative embodiment fordetermining the temperatures of a plurality of multiplexed heaters.

FIGS. 30A through 30D depict examples of measurement configurations fora method for determining the temperatures of a plurality of multiplexedheaters.

FIG. 31 depicts a timing diagram for controlling switches to perform amethod for determining the temperatures of a plurality of multiplexedheaters.

FIG. 32 depicts a chart illustrating the result of non-linear techniquesfor determining the temperatures of a plurality of multiplexed heaters.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Polymerase chain reaction (PCR) is one of the most common and criticalprocesses in molecular diagnostics and other genomics applications thatrequire DNA amplification. In PCR, target DNA molecules are replicatedthrough a three phase temperature cycle of denaturation, annealing, andextension. In the denaturation step, double stranded DNA is thermallyseparated into single stranded DNA. In the annealing step, primershybridize to single stranded DNA. In the extension step, the primers areextended on the target DNA molecule with the incorporation ofnucleotides by a polymerase enzyme.

Typical PCR temperatures are 95° C. for denaturation, 55° C. forannealing, and 72° C. for extension. The temperature at a step may beheld for an amount of time from fractions of a second to severalseconds, as shown in FIG. 1. In principle, the DNA doubles in amount ateach cycle, and it takes approximately 20 to 40 cycles to complete adesired amount of amplification. To have good yield of target product,one has to control the sample temperatures at each step to the desiredtemperature for each step. To reduce the process time, one has to heatand cool the samples to desired temperature very quickly, and keep thosetemperatures for the desired length of time to complete the synthesis ofthe DNA molecules in each cycle. This can be accomplished using amicrofluidic chip and thin-film heaters.

As shown in FIGS. 2 and 3, a microfluidic device 200 embodying aspectsof the present invention may comprise several microfluidic channels 202extending across a substrate 201. Each channel 202 may include one ormore inlet ports 203 (the illustrated embodiment shows three inlet ports203 per channel 202) and one or more outlet ports 205 (the illustratedembodiment shows one outlet port 205 per channel 202). Each channel maybe subdivided into first portion extending through a PCR thermal zone204 (as described below) and a second portion extending through athermal melt zone 206 (as described below). A sipper 208 can be used todraw liquid into the several microfluidic channels 202.

The microfluidic device 200 further includes heater elements in the formof thin film resistive heaters 212. In one embodiment, a heater element212 is associated with each microfluidic channel 202 and may be locatedbeneath the microfluidic channel 202. Each heater element 212 comprisestwo heater sections: a PCR heater 212 a section in the PCR zone 204 anda thermal melt heater section 212 b in the thermal melt zone 206. In oneembodiment, heater electrodes 210 provide electrical power to theseveral thin-film heaters 212 a and 212 b. In the embodiment shown inFIG. 2, the microfluidic device has separate electrical circuits andcontacts for controlling independently the temperature of eachmicrofluidic channel in the PCR and thermal melt zones 204, 206. In thisillustrated embodiment, each area has eight microfluidic channels andeight heaters, with eight individual contacts per zone plus a commonelectrical contact for each zone. Embodiments having other than eightchannels are contemplated as well.

As shown in FIG. 3, the microfluidic device 200 can comprise severaldifferent layers. The microfluidic channels 202 can be etched in achannel layer 302. According to some embodiments, the channel layer 302may comprise fused silica and have a thickness of about 200 μm. Ofcourse, other layer thicknesses may be used as well. A polymer gluelayer 304 may connect the channel layer 302 to a protective layer 306.According to some embodiments of the present invention, the protectivelayer is formed from SiO₂ and has a thickness of approximately 1-2 μm.Glue layer 304 may comprise sheet material with features formed thereincorresponding to the channels 202 and ports 203, 205. Alternativeadhesive layers may be formed by UV curable optical adhesives such as,for example, Norland NOA 72.

Electrical conductor layer 308 may comprise a plurality of heaterelectrodes 210 connected to the various thin-film heaters 212 a and 212b of thin-film heater layer 310. Heater electrodes 210 may include PCRsection leads 318, a PCR section common lead 316 a, thermal melt sectionleads 320, and a thermal melt section common lead 316 b. According toone embodiment of the present invention, one of the PCR section leads318 is connected to one end of each of the thin-film PCR heaters 212 a.A PCR common lead 316 a is connected to the other end of each of the PCRheaters 212 a. Similarly, one of the thermal melt section leads 320 andthermal melt section common lead 316 b is connected to either end ofeach thermal melt heater 212 b. While FIG. 3 shows the electricalconductor layer 308 and the heater layer 310 as separate layers, itwould be understood by one of ordinary skill in the art that they couldalso comprise the same layer.

According to some embodiments of the present invention, the thin-filmheater layer can be resistive materials of Pt, Al, Al₂N₃, Ni, ITO,Ni/chromium, etc.

In one embodiment, a platinum thin-film heater is used with depositionthickness in the range of approximately 10 to 5000 Angstroms, or morepreferably within the range of approximately 50 to 1000 Angstroms.Typical heater film resistance values range from approximately 200 to800 μΩ-cm, or approximately 20 to 1000Ω total resistance, or preferablyapproximately 50 to 250Ω total resistance. The exact composition ofthin-film heater material can be optimized by taking into account thepeak drive currents, overall trace resistances achievable, and designstability/durability.

Another alternate embodiment could incorporate the thin-film heaterresistor layer and a separate nearby resistor trace for measuring thenearby heat by the TCR characteristics of the resistor layer.

The heater electrodes 210, including PCR section leads 318, thermal meltsection leads 320, and common leads 316 a and 316 b, can be composed ofvarious materials ordinarily used as thin-film electrodes such as, forexample, Al, Ag, Au, Pt, Cu, etc. Electrode formation can be, forexample, by evaporation with a desired shape, size, and thickness. Theelectrodes can also be prepared by conventional sputtering process suchas, for example, in an Ar gas atmosphere.

In one embodiment, a protective layer 312 separates the thin film heaterlayer 310 from the substrate layer 314. The protective layers 306 and312 may be made from SiO₂ and can be prepared by conventional plasmaCVD, or sputtering. The SiO₂ thickness can range from approximately 1-3μm. A film layer made of Si:N can be formed by conventional plasma CVD.In one embodiment, the protective layer facilitates microchannelbiocompatibility to enable efficient PCR processes by isolating thereaction channel from the thin-film heaters 212 a and 212 b and theheater electrodes 210.

FIG. 4 shows a partial view of microfluidic device 200 showing a singlechannel 202 in detail. As illustrated in FIG. 4, the single channel 202includes the channel layer 302, the heater electrodes 210, thin filmheater 212 and protective layer 306. The microfluidic channel and thinfilm heater can be created having suitable dimensions for performing PCRand high resolution thermal melt reactions. In one exemplary embodiment,the microfluidic channel 202 dimensions can be approximately 10 μm×180μm and the thin-film heater 212 beneath the microfluidic channel 202 canbe approximately 150 μm wide at the bottom of the channel. Othermicrofluidic channel dimensions can be used as well such as, forexample, approximately 10 μm×300 μm, or more. Other thin film heaterdimensions could be used such as, for example, from approximately 30 μmwide to 300 μm wide (i.e. the full width of the channel in oneembodiment), or more.

FIG. 4 shows a portion of the device 200 at which a thin-film heater 212is overlapped by one of the electrodes 210. Other embodiments may alsoinclude dual thin-film heaters running down the channel in parallel.Such a design would be optimized at normalizing the thermal temperaturedistribution within the microfluidic channel 202.

Referring now to FIG. 5, a functional block diagram of a system 500 forusing a microfluidic device 200 is illustrated. The DNA sample is inputin the microfluidic chip 200 from a preparation stage 502. Thepreparation stage 502 may comprise appropriate devices for preparing thesample 504 and for adding one or more reagents 506 to the sample. Oncethe sample is input into the microfluidic chip 200, e.g., at an inputport 203 or via sipper tube 208, it flows through a channel 202 into thePCR zone 204 where PCR takes place. That is, as explained in more detailbelow, as the sample flows within a channel 202 through the PCR zone204, it is exposed to the temperature profile as shown in FIG. 1 aplurality of times to effect PCR amplification. Next, the sample flowsinto the thermal melt zone 206 where a high resolution thermal meltprocess occurs. Flow of sample into the microfluidic chip 200 can becontrolled by a flow controller 508. A control system 550 may comprise aflow controller 508, a PCR zone temperature controller 510, a PCR flowmonitor 518, a thermal melt zone temperature controller 524, and a zonefluorescence measurement system 532.

The temperature in the PCR zone 204 can be controlled by the PCR zonetemperature controller 510. The PCR zone temperature controller 510,which may be a programmed computer or other microprocessor, sendssignals to the heater device 512 (e.g., a PCR heater 212 a) based on thetemperature determined by a temperature sensor 514 (such as, forexample, an RTD or thin-film thermistor, or a thin-film thermocouplethermometer). In this way, the temperature of the PCR zone 204 can bemaintained at the desired level. According to some embodiments of thepresent invention, the PCR zone 204 may also be cooled by a coolingdevice 516 (for example, to quickly bring the channel temperature from92° C. down to 55° C.), which may also be controlled by the PCR zonetemperature controller 510. In one embodiment, the cooling device 516could be a peltier device, heat sink or forced convection air cooleddevice.

The flow of sample through the microfluidic channels 202 can be measuredby a PCR zone flow monitoring system 518. In one embodiment, the flowmonitoring system can be a fluorescent dye diffusion imaging andtracking system illustrated in U.S. patent application Ser. No.11/505,358, incorporated herein by reference. According to oneembodiment of the present invention, the channels in the PCR zone can beexcited by an excitation device 520 and light fluoresced from the samplecan be detected by a detection device 522. An example of one possibleexcitation device and detection device forming part of an imaging systemis illustrated in U.S. patent application Ser. Nos. 11/606,006 and11/505,358, incorporated herein by reference.

The thermal melt zone temperature controller 524, e.g. a programmedcomputer or other microprocessor, can be used to control the temperatureof the thermal melt zone 206. As with the PCR zone temperaturecontroller 510, the thermal melt zone temperature controller 524 sendssignals to the heating component 526 (e.g., a thermal melt heater 212 b)based on the temperature measured by a temperature sensor 528 which canbe, for example, an RTD or thin-film thermocouple. Additionally, thethermal melt zone 206 may be independently cooled by cooling device 530.The fluorescent signature of the sample can be measured by the thermalmelt zone fluorescence measurement system 532. The fluorescencemeasurement system 532 excites the sample with an excitation device 534,and the fluorescence of the sample can be detected by a detection device536. An example of one possible fluorescence measurement system isillustrated in U.S. patent application Ser. Nos. 11/606,006 and11/505,358, incorporated herein by reference.

In accordance with aspects of the present invention, the thin filmheaters 212 function as both heaters and temperature detectors. Thus, inone embodiment of the present invention, the functionality of heatingelement 512 and 526 and temperature sensors 514 and 528 can beaccomplished by the thin film heaters 212.

In one embodiment, the system 500 sends power to the thin-film heaters212 a and/or 212 b, thereby causing them to heat up, based on a controlsignal sent by the PCR zone temperature controller 510 or the thermalmelt zone temperature controller 524. The control signal can be, forexample, a pulse width modulation (PWM) control signal, as shown in FIG.6. An advantage of using a PWM signal to control the heaters 212 is thatwith a PWM control signal, the same voltage potential across the heatersmay be used for all of the various temperatures required. In anotherembodiment, the control signal could utilize amplitude modulation oralternating current. It is advantageous to use a control signal that isamplitude modulated to control the heaters 212 because a continuousmodest change in voltage, rather than large voltage steps, avoids slewrate limits and improves settling time. Further discussion of amplitudemodulation can be found in U.S. Ser. No. 12/825,476 filed Jun. 29, 2010,which is incorporated herein by reference in its entirety. For purposesof the present invention, amplitude modification is an appropriatealternative to or substitute for, PWM. Thus, throughout the presentspecification, any description written with reference to PWM is equallyapplicable to amplitude modification, and the present inventionspecifically includes methods, systems and devices that utilizeamplitude modification in place of PWM as described herein. As shown inFIG. 6, the desired temperature for the heaters is reached by changingthe duty cycle of the control signal. For example, the duty cycle of thecontrol signal for achieving 95° C. in a PCR heater might be about 50%as shown in the first curve in FIG. 6. As the desired temperaturedecreases, so does the duty cycle. For example, when the desiredtemperature is 72° C., the duty cycle might be around 25% as shown inthe third curve of FIG. 6. When the desired temperature is 55° C., theduty cycle might be only around 10%, as shown in the second curve ofFIG. 6.

According to one embodiment of the present invention, each thin-filmheater 212 a or 212 b can be independently controlled. Independentcontrol of the thin-film heaters permits the various heaters to besupplied with different amounts of power which may be desired tomaintain the desired set temperature. For instance, in a non-limitingexample, the edge-most heaters of the device 200 may require more powerthan the inner most heaters in order to maintain the same temperature.Individual control of the heaters also has the advantage of allowing theheaters to be multiplexed, as illustrated in FIGS. 7 and 8. Multiplexingthe thin-film heaters 212 allows for a balanced energy drain from thepower source and mitigates heat build up in the substrate 314.

As shown in FIG. 7, the heater signals may be multiplexed one after theother in succession. For instance, the falling edge of the control pulsefor microfluidic channel 1 may occur at the same time or after therising edge for channel 2's control pulse, and the rising edge forchannel 3's control pulse could occur at the same time or after thefalling edge of channel 2's control pulse and so on. In anotherembodiment, as shown in FIG. 8, several of the channels may be driven atthe same time. For instance, FIG. 8 shows channels 1, 3, 5 and 7 beingdriving at the same time and channels 2, 4, 6 and 8 being driven at thesame time. While a 50/50 duty cycle is shown for illustration purposesonly, actual duty cycles would change based on the desired temperature.FIG. 9 shows the representative thermal response to the differentialdrive method whereby the CH1 and CH2 channels are thermally out ofphase. Such a method is aimed at distributing the thermal energy withPWM so that the base temperature rise of the substrate chip material isminimized.

Individual microfluidic devices 200 can vary from chip to chip. Thus, toimprove the temperature set-point accuracy for each chip, the controlsystem for the microfluidic device 200 can be calibrated. As shown inFIG. 10, according to one embodiment of the present invention, a method1000 for calibrating a microfluidic device prior to use is provided. Themicrofluidic device is first inserted into the system 500 at step 1002.The control system 550 then applies a constant current to all of theheater electrodes 210 at step 1004. Next, at step 1006, the voltage dropacross each of the thin-film heaters 212 can then be measured todetermine individual resistance (R) values. Using the individual Rvalues, a nominal heater power (P) can be determined to achieve therequired channel temperatures for each microfluidic channel 202 at step1008. Next, the nominal power P is applied to each of the thin-filmheaters for a predetermined time at step 1010. In one embodiment, thepredetermined time can be from approximately 5 μs to 30 ms, and ispreferably approximately 100 μs.

The temperature of the thin-film heater 212 a or 212 b is next monitoredby measuring the changing resistance as the thin-film heater 212 coolsat step 1012. From the data collected at step 1012, a thermal decay timeconstant for each thin film heater 212 can then be calculated at step1014 and an optimal PWM modulation frequency can be calculated based onthe thermal decay time constant at step 1016. The thermal decay timeconstant may be determined, for example, by taking two or moretemperature readings separated in time after heating power is stopped.With the heating power off, the temperature of the heater will begin todrop. The initial rate of temperature decay, in terms of degrees perunit time, may be calculated, for example, from two data points throughsimple algebra, through three or more data points by linear regression,or to many data points through a more complex model through curvefitting. Then, the digital drive signal to the heater should be adjustedto be at a high enough frequency to result in an acceptably small dropin temperature between consecutive pulses. The thermal decay timeconstant values are then stored in memory at step 1018. The calibrationmethod can be used to calibrate the control system 550 for both the PCRzone 204 and the thermal melt zone 206.

In one embodiment, the calibration pulse time is between approximately10 μs to 10 ms, more preferably between approximately 200 μs to 2 ms,and most preferably approximately 500 μs. The heater electroderesistance measurement collection time is between approximately 1 μs to1000 μs, more preferably between approximately 10 μs to 100 μs, and mostpreferably approximately 25 μs. The sampling rate for collecting theheater electrode resistance measurements is between approximately 0.1 μsto 1000 μs, more preferably between approximately 1 μs to 10 μs, andmost preferably approximately 2.5 μs.

FIG. 11 illustrates a method of temperature cycling 1100 to achieve PCRusing calibration data collected using method 1000. Calibration data1102 is retrieved from memory at step 1104. At step 1106, theappropriate PWM signal (based on the calibration data) is next appliedto each of the heater electrodes to achieve the desired temperature ofthe current PCR step. At step 1110, the temperature of the heaters ismeasured and compared to the desired temperature for the current PCRstep 1108 and the PWM modulation parameters 1112. According to oneembodiment, the temperature can be measured between PWM pulses asdescribed below. At step 1114, it is determined whether the appropriatetemperature has been achieved. If it has not been achieved, then themethod returns to step 1106. If it has been achieved, then the PWMsignal is adjusted to maintain the temperature for the appropriate holdtime for the current PCR step at step 1118 using the PCR step hold time1116 and the PWM modulation parameters 1120. At step 1122, the methoddetermines whether the appropriate hold time has been achieved. If thehold time has not been achieved, then the method returns to step 1118.If the appropriate hold time has been achieved, then, at step 1124, themethod indexes to the next PCR step. At step 1126, it is determinedwhether an entire PCR cycle has been completed. If not, then the methodreturns to step 1106. If it has been completed, then the methoddetermines whether the appropriate number of cycles have been completedand returns to step 1104 if not.

In addition to heating the microfluidic channel 202, thin film heaters212 a and 212 b can measure the temperature of the microfluidicchannels. To do so, the thin film heaters 212 a and/or 212 b arepreferably constructed from a material with an electrical resistancethat changes with temperature, such as platinum, Al, ITO, Cu, Ni and Nialloys. Thus, temperature can be derived from the determined resistanceof the heater. The measured temperature can be used in a closed loopfeedback controller.

In one embodiment, the power delivered to the thin-film heaters 212 ismodulated using a digital transistor switch instead of an analogvoltage. As illustrated in FIG. 12, digital transistor switch 1206 maybe a FET, and preferably may be a MOSFET. The control system varies theduty cycle (i.e., pulse width) of the drive signal to regulate powerdelivered to the thin-film heaters. When the transistor 1206 is ON, thecontrol circuit can measure the current delivered to the heat trace R2(comprising the PCR or thermal melt leads 318 or 320, a thin film heater212 a or 212 b, and a common lead 316 a or 316 b and represented as R2in FIG. 12). By knowing the current and voltage across the trace R2,control system 550 can calculate the impedance of R2. Next, the controlsystem can use a formula (e.g., Callendar-Van Dusen) to convert theimpedance value to a temperature value so the control system 550 canmove and hold the temperature as required for the PCR assay.

It may, however, also be desirable to measure the current when thetransistor is OFF. This is because when the transistor is in the ONstate the thin-film heaters 212 heat up very rapidly, and the thin-filmheaters 212 may be several degrees hotter than the fluid in themicrofluidic channels 202. If the system overshoots the desiredtemperature and the water forms micro bubbles in the channel, thecontrol system has difficulty because there is an insulating gas layerbetween its sensor and the load which causes a delay in feedbackcontrol. Another problem with the gas bubble is it has the potential togreatly expand causing flow to be uncontrollable in the micro channels.

Thus, in accordance with another aspect of the present invention, animproved design allows temperature measurement when the transistor is inboth the OFF and ON states. In one embodiment, this can be accomplishedby having a small current flowing through R2 even when the transistor isOFF. A drive system for permitting temperature measurement when thetransistor is in both the OFF and ON states according to one embodimentof the present invention is illustrated in FIG. 12. In FIG. 12, aschematic of the PWM driver and measurement circuit 1200 is shown inwhich the transistor 1206 is connected to R2, which represents thecombined resistance of the thin-film heaters 212 a or 212 b and theleads connected to it (i.e. 316 a and 318 or 316 b and 320). The voltagedrop across R2 can be measured at measurement node 1202. The PWM drivesignal is sent to the gate of the transistor 1206 _(G) at drive signalnode 1204. A large value resistor R10 short circuits the drain 1206 _(D)and the source 1206 _(S). Preferably, R10 will be much larger (e.g., anorder of magnitude or more) than R2. When the transistor 1206 is ON,then current will flow through R2, substantially as normal, and thevoltage drop across R2 can be measured at measurement node 1202. Thevoltage drop across R2 can also be measured when the transistor 1206 isin the OFF state because of large value transistor R10 will allow asmaller current to flow through R2.

Due to the small current resulting from the large value of R10, the selfheating of R2 will be small, so the temperature measured by the trace R2will be close to the temperature of the fluid in the channel. Thecontrol system 550 can be configured to know when the transistor is ONand OFF, so it can use two different formulas to calculate thetemperature. For instance, when the transistor is ON, R9 and transistor1206 are in series and together are in parallel with R10, so the formulafor calculating the resistance of R2 is:

$\begin{matrix}{R_{2} = \frac{R_{{({9 + {RdsON}})}//10}\left( {V_{CC} - V_{measured}} \right)}{V_{measured}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where R_((9+RdsON)//10) represents the equivalent resistance of R10, R9and the resistance of the transistor 1206.

When the transistor is OFF, R10 is in series with R2, so the formula is:

$\begin{matrix}{R_{2} = \frac{R_{10}\left( {V_{CC} - V_{measured}} \right)}{V_{measured}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

where V_(measured) is measured at node 1202.

From the resistance of trace R2, the temperature of R2 can be determinedby, e.g., applying the Callendar-Van Dusen equation, and the temperatureof R2 can be used in a control loop for regulating power to the heater.

Because the microfluidic device 200 can have more than one microfluidicchannel, channel cross talk can be an issue during OFF measurements.That is, if the power to one heater is off while power to an adjacentheater is on, there may be thermal and electrical cross talk between theheater(s) with power on and the heater(s) with power off, therebyaffecting the temperatures derived for the power-off heaters. Eachchannel still needs individual control to maintain an even temperaturedistribution among the PCR area. The potential for crosstalk can beminimized by configuring the control system to make sure all channelsare in the same state during the OFF measurements, as shown in FIG. 13.For example, according to one embodiment, all of the channels can be ata fixed PWM repetition rate, with only the duty cycle of the controlsignal being different for each channel to control the power to eachchannel. A maximum duty cycle (e.g., 90 percent) can be set and allchannels can be measured in the FET OFF state in the remaining time(e.g., 10 percent). Similarly, a minimum duty cycle of 10% could be usedto measure all channels in the FET ON state.

According to one embodiment of the present invention, the controller 550can use a PID feedback equation to change the power output to theheaters 212 a, 212 b to meet the power requirements for the PCR profile.In order to use PID feedback, the system can first be calibrated bysetting the output to a fixed power level and measuring the temperature.This can be done at several temperatures to develop an equation forvoltage to temperature conversion. Alternatively, the Callendar-VanDusen equation, as set forth below, may be used:

R _(T) =R(0° C.)(1+AT+BT ²)  Equation 3

where B is zero for the operating range to the microfluidic device 200.The equation thus can be solved for temperature as follows:

$\begin{matrix}{T = \frac{R_{T} - R_{0}}{{AR}_{0}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Where A is found by the following equation:

$\begin{matrix}{A = \frac{{R\left( {100{^\circ}\mspace{14mu} {C.}} \right)} - {R\left( {0{^\circ}\mspace{14mu} {C.}} \right)}}{100{R\left( {0{^\circ}\mspace{14mu} {C.}} \right)}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Typically, for platinum wires, A≈0.004.

Once the system is calibrated, the temperature can be measured by thecontroller 550 and the PID feedback equation can be used to change thepower to meet the desired PCR profile. The PID feedback equation isgiven by:

Output=K _(p)Error+K _(i)∫Error(dt)+K _(d) d(Error)/dt  Equation 6

The coefficients Kp, Ki, and Kd can be determined by a temperature stepresponse.

According to some embodiments, the heater controller 550 is a firstorder system with no time delay, so K_(d)=0. Kp=1/(Ba*τ) where τ is thetime it takes a heater 212 a or 212 b to cool from a hot temperature toa cool temperature and Ba is the system gain. According to someembodiments, the hot temperature is 95° C. and the cool temperature is54° C. Preferably, τ is about 0.4 and the system gain is about 2.5. Kican be set to the τ to provide moderate control speeds with littleovershoot. For more aggressive speeds, Ki can be set to some fraction ofτ such as τ/5, though doing so may result in the system havingover/undershoot. According to an alternative embodiment of the presentinvention, τ can be the time a heater 212 a or 212 b takes to heat upfrom a cool temperature (e.g. 54° C.) to a hot temperature (95° C.)

As stated above, the heater signals can be multiplexed in differentways. Multiplexing a plurality of heater control signals results in aresistance network such as that shown in FIG. 14, for example. FIG. 14represents the resistance network of an 8-channel microfluidic deviceaccording to one embodiment. In addition to the resistance of theplurality of thin-film heaters 212 a and 212 b (in this example: x1, x2,. . . , x8), there exists a number of parasitic resistances such as, forexample, xc for the common leads 316 a or 316 b and xδ for each of thespaces in 316 a and 316 b that separate thin-film heaters 212 a and 212b. With only independent measurements made at points 1-8, the system maybe underdetermined due to the common lead 316 a or 316 b and otherparasitic resistances. Specifically, even with only 8 measurements theparasitic resistances may result in measurement errors due to system andenvironmental factors. A further aspect of the present inventionutilizes a novel electrical measurement and drive circuit that candetermine the temperature of such multiplexed resistive heaters.

According to embodiments of the present invention, PCR thermocycling isachieved by using resistive traces (such as, for example, platinum thinfilms) as thin film heaters 212 a, 212 b. Thin film heaters can also actas resistance temperature detectors (RTDs). As described above, toachieve fast response and increased measurement sensitivity, eachheating element can be switched into separate “drive” or “measurement”states through the use of a switch (such as a transistor, relay, etc.).The “drive” state uses a lower resistance sense resistor in the voltagedivision circuit to maximize the current through the resistive heaterand achieve fast heating rates. The “drive” state may or may not be usedin conjunction with pulse width modulation (PWM). The “drive” state isalso referred to as the “power on” state. The “measurement” state uses amoderate sense resistance to maximize measurement sensitivity (whileminimizing self heating). The “measurement” state is also referred to asthe “power-off” state.

In one embodiment of the present invention, two more switches perresistive heater are added as well as a common power supply switch thatin combination allow for greater measurement flexibility and efficacy.Additionally, “open” and “supply” states are added to each channel.Furthermore, the common power supply may be included in the “open” or“closed” configuration. These modifications allow the power supply to bemoved from the common lead to any lead desired. This allows the commonlead parasitic resistance to be removed from the measurement in certainconfigurations. Further, by making additional measurements the parasiticresistances can be explicitly determined, which removes a potentialmeasurement error.

A representative drive circuit 1500 capable of making these measurementsis illustrated in FIG. 15. In this embodiment, switching is accomplishedwith electric switches (1502, 1504, 1506, 1508, 1510, 1512), which canbe Metal Oxide Semiconductor Field Effect Transistors (MOSFET) switchesthat are driven by digital output lines on a high speed data acquisitionsystem. FETs 1508 and 1512 have specifically been included as levelshifting devices to increase the voltage at the gate of the primaryswitching FETs 1506 and 1510, respectively, which results in lower ONresistance switching and higher quality measurements. FIG. 15 shows thecircuit for only one of the eight resistive heaters (e.g., resistiveheater 1514) and the common lead.

Circuit branch 1513 may comprise electric switch 1512 and 1510 and maybe used to connect or disconnect the common lead to or from power source1518. Circuit branch 1507 includes electric switches 1506 and 1508 andcan connect or disconnect resistive heater 1514 to or from the drivecircuit branch 1503. Drive circuit branch 1503 is similar to the circuitshown in FIG. 12. Measurement circuit branch 1505 includes electricswitch 1504 and shunt resistor R187, which acts as a shunt around switch1504 when switch 1504 is OFF. With the transistor 1504 ON, theresistance measurements can be taken as normal. When transistor 1504 isOFF, however, then resistance measurements can still be taken due to thesmall current that still flows through large resistor R187.

Each of the remaining heater channels RZ1-10 to RZ2-16 also includescircuit branch 1507, drive circuit branch 1503 and measurement circuitbranch 1505. With drive circuit 1500, the common lead can bedisconnected from the power sources, each heater channel can beselectively connected to the power source, and each heater channel canbe selectively removed from the resistive network. Drive circuit 1500thus allows for isolated, power-on and power-off measurements.

With a plurality of channels the measurement combination possibilitiesare immense. In one embodiment, measurements can be made for the seriesresistance of any two resistors (common lead included), where the numberof combinations is given by:

$\begin{matrix}{C = \frac{\left( {n + 1} \right)!}{2 \cdot {\left( {n - 1} \right)!}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

where n is the number of thin film heaters 212 (common lead excluded).The actual number of measurements required can be determined by personsof ordinary skill given their need for accuracy and the limitations ofthe data logging system.

Considering a resistive network with 8 heating elements (as shown inFIG. 14), resistance measurements of a subset of all of the possiblemeasurements can be represented with a measurement matrix, such as A,which is shown below. The columns of A denote resistances, and the rowsdenote individual measurements. The product of A with the resistancevector x is equal to the measurements made during thermal control,vector b.

$\begin{matrix}{\mspace{20mu} {{Ax} = b}} & {{Equation}\mspace{14mu} 8} \\{\mspace{20mu} {x = {{{inv}(A)}b}}} & {{Equation}\mspace{14mu} 9} \\{\mspace{20mu} {{{Where}\text{:}\mspace{14mu} A} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 7 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 6 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 5 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 4 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 3 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 2 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1\end{bmatrix}}} & \; \\{\mspace{20mu} {x = \begin{bmatrix}x_{1} & x_{2} & x_{3} & x_{4} & x_{5} & x_{6} & x_{7} & x_{8} & x_{c} & x_{\delta}\end{bmatrix}^{\prime}}} & \; \\{b = {{vector}\mspace{14mu} {of}\mspace{14mu} {measurements}\mspace{14mu} {recorded}\mspace{14mu} {through}\mspace{14mu} {data}\mspace{14mu} {acquisition}}} & \;\end{matrix}$

The individual resistances x can be determined through matrix inversion.However, the great flexibility of the measurement circuit and thisalgorithm allows for more measurements than unknowns, resulting in anoverdetermined system. This overdetermined system can then be solved foran optimal solution that reduces the effect of random measurementerrors. In one typical embodiment, the linear least squares technique isused to determine the optimal solution yielding estimates for all heaterresistances along with the parasitic resistances xc and xδ. Finally,each resistor's resistance versus temperature calibration curve(typically of the form R(T)=R(T₀)(1+αΔT)) is used to determine itstemperature, where R(T)=resistance at temperature T, R(T₀)=resistance attemperature T₀ and α=the temperature coefficient of resistivity of theparticular material.

The subset of resistance measurements may be taken according to avariety of different methods. FIGS. 16-21 illustrate several of themethods for taking resistance measurements in accordance with variousembodiments. In method 1600 illustrated in FIG. 16, each resistance ofeach heater 212 a or 212 b can be measured in series with the commonlead 316 a or 316 b, at step 1602. Next, at step 1604, the power supplyV_(cc) is disconnected from the common lead. The power supply is thenconnected to heater n−1, and the voltage drop is measured at heater n atstep 1606. Next, at step 1608 a system of linear equations for 8 heaterresistances and 1 parasitic resistance can be solved. Each resister's Rvs. T calibration data is used to determine the temperature of theresistor at step 1610.

FIG. 17 illustrates a method 1700 in which, at step 1702, each of theheaters 212 a or 212 b is measured in series with the common lead 316 aor 316 b. The power supply is then disconnected from the common lead atstep 1704. Next, at step 1706, the power supply is connected to heater 1and the voltage drop is measured at the n^(th) heater. At step 1708, thepower supply is then connected to the (n−1)^(th) heater and the voltagedrop at heater n is measured. Next, at step 1710, a system of linearequations for 8 heater resistances and 2 parasitic resistances can besolved. At step 1712, each resistor's R vs. T calibration can then beused to determine the temperature.

FIG. 18 illustrated method 1800 in which, at step 1802, each heater ismeasured in series with the common lead. At step 1804, the power supplyis then disconnected from the common lead and a counter variable i isset to 1. At step 1806, the power supply is then connected to heater iand the voltage is measured at heater i+1. At step 1808, it isdetermined whether i+1=n. If not, then the counter is incremented andthe next measurements are taken at step 1806. If i+1 is equal to n, thenthe over determined system can be solved with optimization techniques atstep 1810. Finally, at step 1812, each resistor's R vs. T calibration isused to determine its temperature.

FIG. 19 illustrates method 1900 which is similar to method 1800 butincludes additional steps. As in the method illustrated in FIG. 18, eachheater is measured in series with the common lead at step 1902. Thepower supply is then disconnected from the common lead at step 1904, andi is set to equal 1. Next, at step 1906, the power supply is connectedto heater i, and the voltage drop at heater i+1 is measured. This isrepeated until i+1=n, as shown at step 1908. If not, then i isincremented and step 1906 is repeated. If i+1 does equal n, then i isreset to one and the power supply is connected to heater i+1 and thevoltage drop at heater i is measured at step 1910. This is repeated fori=1 to n. At step 1912, it is determined whether i+1=n. If not, i isincremented by 1 and the process returns to step 1910. Otherwise, theprocess continues to step 1914. At step 1914, the overdetermined systemcan be solved with optimization techniques. Finally, at step 1916, eachresistor's R vs. T calibration can be used to determine its temperature.

FIG. 20 illustrates method 2000 which can be characterized in that itkeeps the power supply connected to the same heater such as, forexample, heater n. First, each heater is measured in series with thecommon lead at step 2002. Next, at step 2004, the power supply isdisconnected from the common lead, and i is set to 1. Next, the powersupply is connected to heater n, and the voltage drop is measured acrossheaters 1 through n−1 at steps 2006 and 2008. The over-determined systemcan then be solved with optimization techniques, as shown in step 2010.Finally, each resistor's R vs. T calibration can be used to determineits temperature at step 2012.

FIG. 21 illustrates method 2100 in which, at step 2102, each heater ismeasured in series with the common lead. The power supply is thendisconnected from the common lead and a counter variable i is set to 1at step 2104. The power supply is then connected to heater i and thevoltage is measured at heater i+1 at step 2106. At step 2108, it isdetermined whether i+1=n. If not, then the counter is incremented by twoand the next measurements are taken at step 2106. If i+1 is equal to n,then the over determined system can be solved with optimizationtechniques at step 2110. Finally, at step 2112, each resistor's R vs. Tcalibration is used to determine its temperature.

In one embodiment, illustrated in FIG. 22, PWM and PID are used for bothPCR and thermal melt. In this case, different supply voltages, dutycycles, and PID control parameters (the proportional, integral, andderivative terms) can be implemented for the two different processes.For example, a larger supply voltage (e.g. 20 Volts) may be desired forPCR to effect faster response time, while a more modest voltage may bedesired for high resolution thermal melt (HR™) (e.g. 10 Volts) to ensureaccurate temperature measurement. The duty cycles required would bedetermined by the closed loop PID control system and could range from 0to 100%. For example, for the transition from denaturation to annealing(e.g. 95° C. to 55° C.), the duty cycle might initially be reduced to 0%to achieve rapid cooling. The duty cycle would then be increased as theheater temperature approaches the set point, with the exact valuesdetermined using PID. Similarly, for the transition from the annealingto extension phases (e.g. 55° C. to 72° C.), the duty cycle mightinitially be set to 100% to heat quickly. The duty cycle would then bereduced as the set point is approached.

FIG. 22 illustrates a method 2200 of PWM closed loop control of theheaters 212 a or 212 b according to an embodiment of the presentinvention. The method could be used to control the heaters in either thePCR zone 204 (PCR Cycles, Power Supply=20V) or the thermal melt zone 206(high resolution thermal melt, Power Supply=10V). At step 2201, the dutycycle is set to some initial value (e.g., 50%) and the PWM frequency isalso set to an initial value (e.g., 1 kHz). The FET or FETs can then beturned ON at step 2202 and the voltage across the heaters 212 a or 212 bmeasured at step 2204. The ON equation (equation 1, above), can then beused to calculate R2 (see FIG. 12). Next, at 2208, a determination ismade as to whether the FET has been ON long enough for the specifiedduty cycle. If yes, at steps 2210-2214, the FET is turned off, thevoltage drop across the heater 212 a or 212 b can be measured, and theOFF equation (equation 2, above) can be used to determine the value ofR2. At step 2216, the Callendar-Van Dusen equation can be used toconvert R into temperature factoring in the calibration coefficients2220, which may be downloaded from a storage device. Next, at step 2218,a new duty cycle can be calculated using a PID equation factoring in thelast duty cycle 2222, the temperature set point 2224, the error betweenthe set point and the measured temperature 2226, and the controlcoefficients Kp, Ki, and Kd 2228. Finally, the FET is turned back on forthe new duty cycle as control loops back to step 2202.

Alternatively, in another embodiment, closed loop control could be used,but PWM drive could be replaced with analog drive in which heating iscontrolled by varying the voltage rather than the duty cycle. Forexample, FIG. 23 illustrates method 2300 which is an analog closed loopcontrol used to obtain the desired temperature. In accordance with thisembodiment, after start at step 2301, the FET is turned on at step 2302.The power supply voltage is then set to an initial level at 2304. Thevoltage drop across the heater is measured at step 2306 and the ONequation (equation 1, above) is used to find R2 value at step 2308.Next, at step 2316, the Callendar-Van Dusen equation is used to convertthe resistance value into temperature factoring in the calibrationcoefficients 2320. Next, at step 2318, a PID equation is used tocalculate a new supply voltage factoring in the last supply voltage2322, the temperature set point 2324, the error between the temperatureset point and the measured temperature 2326, and control coefficients2328. The new supply voltage is set as control loops back to step 2302.

According to an alternative embodiment, after step 2308, the FET isturned OFF for a fixed amount of time to allow the sensor and the liquidin the microfluidic channel to equalize in temperature at step 2310. Thevoltage drop across the heater is measured at step 2312, and the OFFequation (equation 2, above) is used to calculate R2 at step 2314.

In another embodiment, closed loop control is utilized which involvesusing PWM to heat different resistive heaters differently to account formanufacturing variations or temperature gradients. As illustrated inFIG. 24, different duty cycles could be used for each heater to ensuretemperature uniformity. According to method 2400, the PWM frequency isset to a predetermined frequency (e.g., 1 kHz) at step 2401. Eachchannel's duty cycle is adjusted for uniform temperature at 2402. Next,at step 2404, the supply voltage is set to an initial value. The voltagedrop across the heater is then measured at step 2406, and the ONequation is used to calculate the value of R2 at step 2408. The FET iskept on until the duty cycle time is complete, as determined at step2410. Next, at step 2412, the FET is turned OFF and the voltage dropacross the heater is measured at step 2414. Next, the OFF equation canbe used in step 2416 to find R2. The Callendar-Van Dusen equation canthen be used to convert the resistance value measured for R2 into atemperature value at step 2418 factoring in calibration coefficients2422.

Finally, a PID equation is used to calculate a new supply voltage atstep 2420 factoring in the last supply voltage 2424, the temperaturesetpoint 2426, the error between the temperature setpoint and themeasured temperature 2428, and the control coefficients (Kp, Ki, andKd). The new supply voltage is set as the control loops back to step2404.

In another embodiment, closed loop control could be used for the PCRprocess (as described above), and thermal melt could be performed in anopen loop configuration. As illustrated in FIG. 25, a method of openloop thermal melting would involve increasing the supply voltage througha controllable power supply while monitoring the temperature of theheaters using the measurement control circuit. Another method of openloop thermal melting would involve ramping the duty cycles (e.g. from30% to 80%) while monitoring the temperature of the heaters 212 a, 212b.

In another embodiment, PCR could be performed in open loop configurationwhile thermal melt is performed using PID. For PCR, different drivecurrents and/or duty cycles would be used to achieve differenttemperatures. The different drive currents (which are predetermined) maybe achieved by a programmable power supply or through the use of adigital potentiometer (Rdp), which controls the total resistance andthus the drive current. The PCR drive voltage could be always on (100%duty cycle, i.e. traditional direct current (DC)) or PWM could be usedwith fixed but predetermined duty cycles less than 100%. In thisconfiguration, PWM could also be used to heat different resistiveheaters 212 a, 212 b differently to account for manufacturing variationsor temperature gradients.

According to another embodiment of the present invention, open loopcontrol can be performed by the method 2500 illustrated in FIG. 25. Inthis embodiment, the control signal is given an initial duty cycle(e.g., 50%) at step 2501. Next, at step 2502, the FET is turned ON andthe voltage drop across the heater is measured at step 2504. The ONequation can then be used to determine the value of R2 at step 2506. TheFET is held in the ON state until the appropriate amount of time for theduty cycle has passed, as determined at step 2508. Next, at step 2510,the FET is turned to the OFF state and the voltage drop across theheater is measured at step 2512. The OFF equation can then be used todetermine the value of R2 at step 2514. Callendar-Van Dusen equationscan then be used to convert R2's resistance value into a temperaturevalue in step 2516 using the heater's calibration coefficients 2522.Next, the actual temperatures can be recorded in step 2518, and the dutycycle and/or the analog voltage can be adjusted according to apredetermined power profile in step 2520. The FET is then turned ONagain as control loops back to step 2502.

Additional embodiments of the present invention are described andillustrated as follows in connection with FIGS. 26-32. For example, FIG.26 illustrates a microfluidic device 2600 embodying additional aspectsof the present invention. Microfluidic device 2600 includes severalmicrofluidic channels 202 extending across a substrate 201. Each channel202 includes one or more inlet ports 203 (the illustrated embodimentshows two inlet ports 203 per channel 202) and one or more outlet ports205 (the illustrated embodiment shows one outlet port 205 per channel202). In exemplary embodiments, each channel may be subdivided into afirst portion extending through a PCR thermal zone 204 (as describedbelow) and a second portion extending through a thermal melt zone 206(as described below).

The microfluidic device 2600 further includes heater elements in theform of thin film resistive heaters 212 associated with the microfluidicchannels 202. In the embodiment illustrated in FIG. 26, each heaterelement 212 comprises two heater sections: a PCR heater 212 a section inthe PCR zone 204, and a thermal melt heater section 212 b in the thermalmelt zone 206. In one embodiment, heater electrodes 210 provideelectrical power to the several thin-film heaters 212 a and 212 b. Inthe embodiment shown in FIG. 26, the microfluidic device has separateelectrical circuits and contacts for controlling independently thetemperature of each microfluidic channel in the PCR and thermal meltzones 204, 206.

The microfluidic device 2600 includes a plurality of heater electrodes210 connected to the various thin-film heaters 212 a and 212 b. Heaterelectrodes 210 may include PCR section leads 318, one or more PCRsection common lead 316 a, thermal melt section leads 320, and one ormore thermal melt section common lead 316 b. According to one embodimentof the present invention, a PCR section lead 318 is connected to each ofthe thin-film PCR heaters 212 a.

In the non-limiting embodiment illustrated in FIG. 26, each area haseight microfluidic channels and eight heaters, with eight individualcontacts per zone. Each area also has two common electrical leads. Eachof the two common leads 316 can associated with a separate four of thechannels 212. For example, a PCR common lead 316 a is connected to theother end of four of the PCR heaters 212 a, and the other four of theheaters 212 a are connected to another PCR common lead 326 a. Similarly,a thermal melt section lead 320 and thermal melt section common lead 316b are connected to either end of four thermal melt heater 212 b, and theother four of the heaters 212 b are connected to another thermal meltcommon lead 326 b. This configuration enables independently measuringand controlling the heaters for two separate groups of microfluidicchannels on a single microfluidic device 2600. Furthermore, because eachgroup includes fewer heaters, the methods for performing closed loopthermal control described herein can be performed more quickly and withless computational resources.

In some embodiments, other aspects and features of the microfluidicdevice 2600 correspond with analogous features of the microfluidicdevice 200 described above and will be understood by those having skillin the art with reference to FIGS. 3-4 and the foregoing descriptionthereof.

The microfluidic device 2600 can be used in conjunction with the methodsand systems described above. For example, one can use the microfluidicdevice 2600 in place of the microfluidic chip 200 in connection with thesystem 500 described above to heat and cool DNA samples to desiredtemperature very quickly, and keep those temperatures for the desiredlength of time to complete the synthesis of the DNA molecules in eachPCR cycle. In a non-limiting example, the system 500 can use multiplexedpulse width modulated control signals, as described above with referenceto FIGS. 6-9.

Furthermore, the microfluidic device 2600 can be used with a multiplexeddrive circuit, for example, drive circuit 1500 illustrated in FIG. 15.In some embodiments, the multiplexed drive circuit includes digitalswitches, for example field effect transistors, to effectuate rapidswitching of power and measurement connections.

As described above with reference to FIGS. 10-25, the drive circuit 1500can be used with a microfluidic device, for example microfluidic device200 or microfluidic device 2600, to measure the resistances of heaterelements in the microfluidic device and calibrate the heaters to performaccurate closed loop thermal control of PCR reactions or otherbiological reactions in the microfluidic device.

FIG. 27 illustrates a method 2700 for taking resistance measurements ofelements in a multiplexed resistive network according to anotherembodiment of the present invention. In some embodiments, the method2700 can be used in connection with one or more of the system 500 andthe drive circuit 1500 to measure the resistances of resistive heaters(such as, for example, resistance temperature detectors in thermalcommunication with a fluidic channels) on a microfluidic device, forexample the microfluidic device 200 or the microfluidic device 2600.Furthermore, the measurements of the method 2700 can be performed duringthe OFF portion of a pulse width modulated power signal.

Referring to FIGS. 15 and 27, the method 2700 can begin at step 2704 bydisconnecting the power supply V_(cc) from the common lead (for example,by using switches 1510 and 1512 to disconnect the power supply fromcommon lead ROOM1 of the microfluidic chip illustrated in FIG. 15).Next, at step 2705, the power supply is connected to a first heater h₁(for example, using switches 1506 and 1508 to connect the power supplyto the seventh heater RZ1-15) and the voltage drop is measured atanother heater h₂ (for example, using switch 1504 and the measurementlead Z1,1 to measure the voltage drop at the first heater RZ1-9). Insome preferred embodiments, h₁ and h₂ are selected to ensure that themethod 2700 results in a measurement matrix A, i.e., a measurementmatrix as described above with reference to Equations 8 and 9, that willbe of full rank so that an inverse of A may be calculated.

In order to uniquely determine the resistances of n resistors in anetwork (i.e., in order to solve a system of equations with n“unknowns”), at least n measurements should be taken (i.e., at least nlinearly independent equations should be provided), and each resistormust be included in at least one of the measurements. Thus, in additionto the measurement taken at step 2705, n−1 additional measurements areneeded. Each of the n−1 additional measurements preferably measures adistinct set of resistors so that the measurement matrix A includes nlinearly independent rows. In one non-limiting embodiment describedbelow and illustrated in FIG. 27, a sequence of n−1 measurements aretaken where the resistors for each measurement are selected in a similarmanner to steps 1806-1808 of the method 1800, described above withreference to FIG. 18. That is, an index variable i is set to equal 1. Atstep 2706, the power supply is then connected to heater i and thevoltage is measured at heater i+1. At step 2708, it is determinedwhether i+1=n. If not, then the counter is incremented and the nextmeasurements are taken at step 2706. If i+1 is equal to n, then thesystem can be solved with linear algebra at step 2710. Finally, at step2712, each resistor's R vs. T calibration is used to determine itstemperature.

As will be understood by those having skill in the art, by selecting theheaters h₁ and h₂ in step 2705 so that the measurement matrix A isinvertible, the method 2700 can omit the steps of independentlymeasuring each resistance of each resistive heater 212 a or 212 b inseries with the common lead 316 a or 316 b. Omitting these steps mayreduce the total number of measurements taken and thus decrease theamount of time needed to make the measurements and increase the speed ofthe closed loop thermal control.

A non-limiting example timing diagram for controlling the switches toperform an embodiment of the method 2700 is illustrated in FIG. 28. Asillustrated in FIG. 28, the measurement at step 2705 (for example,measurement #1) may comprise connecting the power supply V_(cc) toresistive heater 7 (e.g., by activating the switches 1506 and 1508 inthe circuit branch 1507 corresponding to the resistive heater 7illustrated in FIG. 15) and measuring the voltage at heater 1 (e.g., byactivating the switch 1504 in the measurement circuit branch 1505corresponding to resistive heater 1 and measuring the voltage at themeasurement node corresponding to heater 1 (e.g., “Z1,1 A/D” in FIG.15)). Performing this measurement at step 2705, followed by themeasurements indicated at steps 2706 through 2708 as described above,will result in the following measurement matrix A:

$A = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 1\end{bmatrix}$

Furthermore, with reference to FIG. 14 and the description thereof setforth above, in some embodiments the additional resistance xδ for eachof the spaces in 316 a and 316 b that separate thin-film heaters 212 aand 212 b may be ignored. Thus, for a system of n multiplexed sensors,there are only n unknowns (i.e., the resistance of each resistive heater212 a or 212 b) and only n measurements are required to completelyspecify these resistances.

As described above in connection with Equation 9, the resistances ofeach heater can be uniquely determined by defining a first matrix bcorresponding to the measurements of each combined series resistance(that is, for example, the measured resistances acquired at steps 2705and 2706), defining a second matrix A (i.e., the measurement matrix)having rows and columns such that each column corresponds to a sensor inthe network and each row represents a measured sensor pairconfiguration, generating an inverse matrix of the second matrix (thatis, generating A⁻¹), and multiplying the inverse of the second matrix bythe first matrix (that is, calculating A⁻¹b). As described above, thesets of heaters selected for the measurements preferably result in asecond matrix A that defines n linearly independent equations (that is,the second matrix A is of full rank).

In some embodiments, different resistive heater pairs may be selected insteps 2705 through 2708, so long as n distinct measurements are taken,where n is the number of resistive heaters to be measured, and thecorresponding measurement matrix A is of full rank (i.e., themeasurements for n resistive heaters specify a system of n linearlyindependent equations). These criteria ensure that the measurement isefficient and does not take longer to complete than necessary, whilesimultaneously ensuring that A is invertible and the system of equationscan be solved using linear algebra to uniquely determine the resistancesof the resistive heaters. These features facilitate rapid closed-loopthermal control.

FIG. 29 illustrates a method 2900 for taking resistance measurements ofelements in a multiplexed resistive network according to anotherembodiment of the present invention. In some embodiments, the method2900 can be used in connection with one or more of the system 500 andthe drive circuit 1500 to measure the resistances of resistive heaterson a microfluidic device, for example the microfluidic device 200 or themicrofluidic device 2600. Furthermore, the measurements of the method2900 can be performed during the OFF portion of a pulse width modulatedpower signal.

FIG. 29 illustrates a method 2900 according to another embodiment of thepresent invention in which the number of measurements is equal to thenumber of heaters, and each heater is measured an equal number of times.Measuring each heater an equal number of times can provide a more equaldistribution of measurement error among the heaters so that themeasurement of any one heater does not have a higher error level thanany of the other heaters.

As described below with reference to FIGS. 29-31, in one embodiment,each of the heaters 212 a or 212 b is measured in series with a parallelcombination of other heaters 212 a or 212 b to create a system ofnonlinear equations describing equivalent resistances. Measurementsaccording to the method 2900 can produce a solvable system of nonlinearequations that measures each sensor the same number of times and onlyrequires a number of measurements equal to the number of heaters.

The method 2900 will be described in detail as follows. At step 2904,the power supply is disconnected from the common lead (for example, byusing digital switches to disconnect the power supply from common lead326 of the microfluidic chip 2600). As described above, for example withregard to the method 2700, before additional measurements are taken, anindex variable i can be initialized to equal 1. At step 2906, the powersupply is connected to the leads for a first set of two or more poweredheaters 212, and the voltage is measured at another measured or sensedheater 212 that is distinct from the powered heaters. This configuration(e.g., a parallel combination of the powered heaters in series with thesensed heater) produces an equivalent resistance that is a non-linearcombination of the resistances of the heaters 212, as shown below inEquation 10:

$\begin{matrix}{R_{eq} = {{\Omega (S)} + \left\lbrack {\sum\limits_{k}\frac{1}{\Omega \left( P^{k} \right)}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

In Equation 10, R_(eq) is the equivalent resistance of the measurement,P is the set of powered heaters, P^(k) is the k^(th) powered heater inthe set P, S is the sensed heater, and Ω(x) represents the resistance ofx. For example, assuming the resistance of the sensed heater is R₄ andthe resistances of the powered heaters are R₁ and R₂, the equivalentresistance can be expressed as:

$\begin{matrix}{R_{eq} = {R_{4} + \left\lbrack {\frac{1}{R_{1}} + \frac{1}{R_{2}}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

As described above with reference to the method 2700, in order touniquely determine the resistances of n resistors in a network, at leastn measurements should be taken. Thus, the measurement step 2906 shouldbe repeated for a total of n times, where each iteration of step 2906preferably measures a distinct network of resistors.

At step 2908, it is determined whether i+1>n. If not, then themeasurement counter i is incremented, a new set of powered heaters P anda new sense heater S are selected, and the next measurement is taken atstep 2906. As described above, digital switches, such as, for example,field effect transistors, can be used to switch the power supply anddata acquisition device to the designated heaters. An advantage of thedigitally controlled system is the ability for closed-loop thermalcontrol. That is, a temperature controller can adjust the heat input asa result of the rapid temperature measurement. Furthermore, byperforming all these measurements during the OFF time of a pulse widthmodulated heating cycle, it is possible to use the sensors as heating aswell as sensing devices.

In some preferred embodiments, each iteration of step 2906 selects thesame number of powered heaters for the set P. For example, in onenon-limiting embodiment illustrated in FIGS. 30A-30D, each measurementstep 2906 incorporates two powered heaters in the set P (e.g., P₁={h₁,h₂}, P₂={h₁, h₄}, P₃={h₃, h₄}, and P₄={₂, h₃}). FIG. 31 illustrates atiming diagram for controlling the switches to perform the method 2900for four of the heaters connected to a common lead 316 a of themicrofluidic device 2600, as illustrated in FIGS. 30A-30D. As shown inFIG. 31, two complete measurement cycles are illustrated.

In accordance with one embodiment, performing measurements according toFIGS. 30A-30D and 31 yields four equivalent resistance measurements andcorresponding equations:

$\begin{matrix}{R_{{eq}\; 1} = {R_{4} + \frac{R_{1} \cdot R_{2}}{R_{1} + R_{2}}}} & {{Equation}\mspace{14mu} 12} \\{R_{{eq}\; 2} = {R_{3} + \frac{R_{1} \cdot R_{4}}{R_{1} + R_{4}}}} & {{Equation}\mspace{14mu} 13} \\{R_{{eq}\; 3} = {R_{2} + \frac{R_{3} \cdot R_{4}}{R_{3} + R_{4}}}} & {{Equation}\mspace{14mu} 14} \\{R_{{eq}\; 4} = {R_{1} + \frac{R_{2} \cdot R_{3}}{R_{2} + R_{3}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

In this embodiment, each heater is measured three times (i.e., twice inparallel with another sensor and once in series with two other parallelsensors).

After n measurements have been taken (that is, after step 2906 has beenrepeated n times), step 2908 determines that i+1 is greater than n. Thesystem of non-linear equations can be uniquely solved with nonlineartechniques at step 2910.

The system of equations 12-15 cannot be solved using linear algebrabecause the equations are non-linear in nature. However, in accordancewith one embodiment, the system can be solved iteratively by making aninitial estimation, serially calculating R1 through R4, and thenrepeating the calculations until the updated values of R1 through R4change by less than some specified tolerance.

For example, in one non-limiting example, the measured equivalentresistances can be:

R_(eq1)=187.50Ω

R_(eq2)=183.45Ω

R_(eq3)=186.75Ω

R_(eq4)=184.65Ω

As illustrated in FIG. 32, with an initial estimation of 100Ω for R1through R4, only 9 iterations are required for the resistances toconverge to a tolerance of less than 0.001Ω.

Finally, at step 2912, each resistor's R vs. T calibration is used todetermine its temperature.

In some embodiments, the sensed heater S may be a set of two or moreheaters distinct from the set of powered heaters P. For eachmeasurement, the set of sensed heaters S and the set of powered heatersP may form a partition of all of the heaters (i.e., each heater is aeither a sensed heater S or a powered heater P). In other embodiments,each measurement may electronically isolate one or more heaters that areneither included as a sensed heater nor included as a powered heater forthat measurement. Generally, the equivalent resistance of the i^(th)measurement may be expressed as:

$\begin{matrix}{R_{{eq}{(i)}} = {\left\lbrack {\sum\limits_{m}\frac{1}{\Omega \left( S_{k}^{m} \right)}} \right\rbrack^{- 1} + \left\lbrack {\sum\limits_{k}\frac{1}{\Omega \left( P_{i}^{k} \right)}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 16}\end{matrix}$

where R_(eq(i)) is the equivalent resistance of the i^(th) measurement,Ω(S_(i) ^(m)) is the resistance of the m^(th) sensed heater in S_(i),and Ω(P_(i) ^(k)) is the resistance of the k^(th) powered heater inP_(i).

In some preferred embodiments, each heater is selected as a poweredheater for an equal number of measurements, and each heater is selectedas a sensed heater for an equal number of measurements. Furthermore,each of the sets P_(i) are respectively unique, and each of the setsS_(i) are respectively unique. Because each heater is measured the samenumber of times in the same fashion, measurement errors will beuniformly distributed.

As will be understood by one having ordinary skill in the art, othercombinations of series and parallel measurements that result in uniformerror are also possible. The desired characteristic is that all sensorsare measured the same number of times and in a similar manner. So, forexample, each sensor could be measured 4 times (3 times in parallel andonce in series):

$\begin{matrix}{R_{{eq}\; 1} = {R_{4} + \left\lbrack {\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 17} \\{R_{{eq}\; 2} = {R_{3} + \left\lbrack {\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{4}}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 18} \\{R_{{eq}\; 3} = {R_{2} + \left\lbrack {\frac{1}{R_{1}} + \frac{1}{R_{3}} + \frac{1}{R_{4}}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 19} \\{R_{{eq}\; 4} = {R_{1} + \left\lbrack {\frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 20}\end{matrix}$

The methods for taking resistance measurements in accordance withvarious embodiments have been described with reference to resistiveheater sensors. As will be understood by one having ordinary skill inthe art, similar methods may be adapted to multiplexed networkscomprising capacitive sensors or inductive sensors.

For example, in additional embodiments, a method for taking inductancemeasurements of N inductors in a multiplexed inductor network, forexample for performing closed-loop thermal control of a microfluidicdevice including inductive temperature sensors, can include measuringthe equivalent inductance of N combination of the inductors, where theequivalent inductance of each combination specifies a non-linearrelationship between the inductors in the combination.

Each combination of inductors can be a partition of the inductors into apowered (or source) set and a sensed (or drain) set. In someembodiments, for each combination some of the inductors may not beincluded in either the source set or the drain set. As described above,digital switches, such as field effect transistors, can be used toconnect each of the inductors in the source set to a source voltage andto connect each of the inductors in the drain set to a drain voltage.Furthermore, digital switches can provide for rapid switching, so thatthe measurement process can be completed, for example, during the offtime of a pulse width modulated power signal.

When a source voltage is applied to the source set of inductors and adrain voltage is connected to the drain set of inductors, the equivalentinductance can be measured and, as long as at least one of the sourceset or drain set includes two or more inductors, the measured equivalentinductance will specify a non-linear relationship between the inductors.For example, when the source set contains two inductors L₁ and L₂, andthe drain set includes two inductors L₃ and L₄, the equivalentinductance will result from a parallel combination of L₁ and L₂ inseries with a parallel combination of L₃ and L₄, which can be expressedas:

$\begin{matrix}{L_{eq} = {\left\lbrack {\frac{1}{L_{1}} + \frac{1}{L_{2}}} \right\rbrack^{- 1} + \left\lbrack {\frac{1}{L_{3}} + \frac{1}{L_{4}}} \right\rbrack^{- 1}}} & {{Equation}\mspace{14mu} 21}\end{matrix}$

After N measurements are taken to obtain N non-linear relationships, thesystem of non-linear equations can be solved to determine the inductanceof each inductor. In some embodiments, the non-linear system ofequations can be solved using an initial estimate and iterativerefinement, as described above with regard to the method 2900.

In some preferred embodiments, each inductor is included in a source setthe same number of times, and each inductor is included in a drain setthe same number of times. Furthermore, in some preferred embodimentseach source set includes the same number of inductors, and each drainset includes the same number of inductors. These features ensure thateach inductor is measured an equal number of times in an equal manner.As discussed above, this condition can provide a more equal distributionof measurement error among the inductor so that the measurement of anyone inductor does not have a higher error level than any of the otherinductor.

In additional embodiments, a method for taking inductance measurementsof N capacitors in a multiplexed capacitor network, for example forperforming closed-loop thermal control of a microfluidic deviceincluding capacitive temperature sensors, can include measuring theequivalent capacitance of N combination of the capacitors, where theequivalent capacitance of each combination specifies a non-linearrelationship between the capacitors in the combination.

As described above, each combination of capacitors can be a partition ofthe capacitors into a powered (or source) set and a sensed (or drain)set. In some embodiments, for each combination some of the capacitorsmay not be included in either the source set or the drain set. Asdescribed above, digital switches, such as field effect transistors, canbe used to connect each of the capacitors in the source set to a sourcevoltage and to connect each of the capacitors in the drain set to adrain voltage. Furthermore, digital switches can provide for rapidswitching, so that the measurement process can be completed, forexample, during the off time of a pulse width modulated power signal.

When a source voltage is applied to the source set of capacitors and adrain voltage is connected to the drain set of capacitors, theequivalent capacitance can be measured and, because a series combinationof equivalent capacitances combines non-linearly, the measuredequivalent capacitance will specify a non-linear relationship betweenthe capacitors. For example, when the source set contains two capacitorsC₁ and C₂, and the drain set includes two capacitors C₃ and C₄, theequivalent capacitance will result from a parallel combination of C₁ andC₂ in series with a parallel combination of C₃ and C₄, which can beexpressed as:

$\begin{matrix}{C_{eq} = \left\lbrack {\frac{1}{C_{1} + C_{2}} + \frac{1}{C_{3} + C_{4}}} \right\rbrack^{- 1}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

After N measurements are taken to obtain N non-linear relationships, thesystem of non-linear equations can be solved to determine thecapacitance of each capacitor. In some embodiments, the non-linearsystem of equations can be solved using an initial estimate anditerative refinement, as described above with regard to the method 2900.

In some preferred embodiments, each capacitor is included in a sourceset the same number of times, and each capacitor is included in a drainset the same number of times. Furthermore, in some preferred embodimentseach source set includes the same number of capacitors, and each drainset includes the same number of capacitors. These features ensure thateach capacitor is measured an equal number of times in an equal manner.As discussed above, this condition can provide a more equal distributionof measurement error among the capacitor so that the measurement of anyone capacitor does not have a higher error level than any of the othercapacitor.

In other aspects of the invention, a microfluidic device is provided forperforming biological reactions according to the various methodsdescribed herein. In one embodiment, a microfluidic device comprises amicrofluidic chip having a plurality of microfluidic channels and aplurality of multiplexed heater electrodes, wherein the heaterelectrodes are part of a multiplex circuit including a common leadconnecting the heater electrodes to a power supply, each of the heaterelectrodes being associated with one of the microfluidic channels, andswitching elements associated with each heater electrode. A suitablemicrofluidic device could be, for example, the microfluidic devicedescribed above in FIGS. 2-4 and 26.

The microfluidic device also includes a control system configured to, inaccordance with one embodiment of the present invention, regulate powerapplied to each heater electrode by varying a duty cycle, control theswitching elements to selectively connect the power supply to a subsetof two or more of the heater electrodes to facilitate measurements ofvoltage drops across the subset of heater electrodes and another of theelectrodes, and determine the temperature each heater electrode bydetermining the resistance of each heater electrode. Furthermore, insome embodiments the control system is also configured to use thetemperature of one or more heater electrodes as a feedback signal toperform closed loop thermal control of the heaters, for example asdescribed in connection with FIGS. 22-24. The control system can be usedto perform PCR or other temperature-dependent biological processes,using the feedback signal from the one or more heaters to determine thestatus of the reaction and adjust the duty cycle of a pulse widthmodulated power signal accordingly. A suitable control system isdescribed above in connection with FIG. 5 and could include, forexample, an appropriately programmed general purpose computer or specialpurpose computer.

In accordance with another embodiment of the present invention, themicrofluidic device also includes a control system configured to providetiming instructions to sequentially measure the combined seriesresistances for n number of distinct sensor pairs, where n is the numberof sensors in the multiplexed network of the microfluidic device, andwherein each of the plurality of sensors is included in at least one ofthe measured sensor pairs. In one embodiment, the control systemsequentially measures the combined series resistances of the n distinctpairs by applying a voltage to a first terminal electrically coupled toat least two sensors connected in series and measuring the voltage at asecond terminal electrically coupled to the at least two sensors.Furthermore, in some embodiments the microfluidic device also includes aprocessor configured to determine the individual resistance of at leastone of the plurality of sensors based upon the measured combined seriesresistances, for example, by generating a measurement matrix having rowsand columns such that each column corresponds to a single sensor in thenetwork and each row describes a measurement configuration applied bythe control unit, and determining the individual resistance of at leastone sensor in the network by multiplying the inverse of the measurementmatrix by a vector containing the measured combined series resistances.

In one embodiment, the control system is also configured to use thetemperature of one or more heater electrodes as a feedback signal toperform closed loop thermal control of the heaters, for example asdescribed in connection with FIGS. 22-24. The control system can be usedto perform PCR or other temperature-dependent biological processes,using the feedback signal from the one or more heaters to determine thestatus of the reaction and adjust the duty cycle of a pulse widthmodulated power signal accordingly.

Embodiments of the present invention have been fully described abovewith reference to the drawing figures. Although the invention has beendescribed based upon these preferred embodiments, it would be apparentto those of skill in the art that certain modifications, variations, andalternative constructions could be made to the described embodimentswithin the spirit and scope of the invention.

1. A method for determining the resistance of a sensor in a multiplexedsensor network including a plurality of sensors sharing a common leadfor connecting each of the plurality of sensors to a power supply,comprising: sequentially measuring the combined series resistances for Nnumber of distinct sensor pairs, such that each of the plurality ofsensors is included in at least one of the measured sensor pairs,wherein N is the number of sensors in the plurality of sensors, and themeasured sensor pairings are such that the individual resistance of eachof the plurality of sensors may be determined; and determining for theindividual resistance of at least one of the plurality of sensors basedupon the measured combined series resistances.
 2. The method of claim 1,wherein the step of determining for the resistance of at least one ofthe plurality of sensors comprises: defining a first matrixcorresponding to the measured combined series resistances; defining asecond matrix having rows and columns such that each column correspondsto a sensor in the network and each row represents a measured sensorpair configuration; generating an inverse matrix of the second matrix;and multiplying the inverse of the second matrix by the first matrix. 3.The method of claim 2, wherein the second matrix is defined by linearlyindependent equations such that the second matrix is of full rank. 4.The method of claim 1, wherein measuring a combined series resistance ofa sensor pair comprises: electrically isolating the sensor pair from theother sensors in the plurality of sensors; applying a source voltage orcurrent to a first terminal electrically coupled to a first sensor ofthe sensor pair, measuring an output voltage at a second terminalelectrically coupled to a second sensor of the sensor pair.
 5. Themethod of claim 4, wherein the measurements are performed in accordancewith timing instructions supplied by a control unit.
 6. The method ofclaim 1, wherein the multiplexed sensor network is a component of amicrofluidic device.
 7. The method of claim 1, wherein the sensors arein thermal communication with a fluidic channel.
 8. The method of claim1, wherein the sensors are resistance temperature detectors.
 9. Themethod of claim 1, further comprising: generating a feedback signalbased upon either the equivalent resistance of a series combination ofsensors or the resistance of an individual sensor; and transmitting thefeedback signal to a control unit configured to provide closed-loopthermal control.
 10. The method of claim 9, wherein the feedback signaldescribes the status of a biological process.
 11. A microfluidic devicefor performing biological reactions comprising: a microfluidic chiphaving a plurality of microfluidic channels and a plurality of sensorelements, wherein the sensor elements are connected in a multiplexednetwork that includes a shared common lead; a control unit configured tosequentially measure the combined series resistances for N number ofdistinct sensor pairs; a processor configured to determine theindividual resistance of at least one of the plurality of sensors basedupon the measured combined series resistances; wherein each of theplurality of sensors is included in at least one of the measured sensorpairs, and wherein N is the number of sensors in the plurality ofsensors, and the measured sensor pairings are such that the individualresistance of each of the plurality of sensors may be determined. 12.The device of claim 11, wherein the processor is further configured todefine a measurement matrix having rows and columns such that eachcolumn corresponds to a single sensor in the network and each rowdescribes a measurement configuration applied by the control unit and,the processor being further adapted to determine the individualresistance of at least one sensor in the network by multiplying theinverse of the measurement matrix by a vector containing the measuredcombined series resistances.
 13. The device of claim 12, wherein themeasurement matrix is of full rank.
 14. The device of claim 11, furthercomprising: a first terminal electrically coupled to at least twosensors connected in series; and a second terminal electrically coupledto the at least two sensors; wherein a voltage or current applied to thefirst terminal generates a current or voltage at the second terminalrepresentative of the combined series resistance of the at least twosensors.
 15. The device of claim 11, wherein the sensors are resistancetemperature detectors.
 16. The device of claim 11, wherein the controlunit is further adapted to heat the resistance temperature detectors bypulse width modulation.
 17. The device of claim 11, wherein the controlunit is further adapted to heat the resistance temperature detectors byamplitude modulation.